Talk:Whole number/Archive 1

Archive 1

Dispute

If there's dispute in the mathematical world as to the meaning of "whole number", why do we present one view as correct? WP:NPOV, anyone? Proteus (Talk) 12:52, 1 June 2006 (UTC)

Not Screwed

The definition for whole number's just happens to be short. It's as simple as 0,1,2,3 etc. 24.12.8.97 20:46, 25 September 2006 (UTC)

Nonsense

This Wikipedia page is completely screwed up. There's absolutely no dispute about the definition of a whole number. Whole number is an integer, which includes 0, all positive and all negative integers. Any decent book on math defines whole numbers in that manner.

There was a well-known dispute about whether 0 should be included into the definition of a 'natural' number. But there has never been a dispute about excluding negative integers from the definition of a 'whole' number.

whole number

whole number Mathematics. Any of the set of numbers including zero and all negative and positive multiples of 1.

Excerpted from The American Heritage Dictionary of the English Language, Third Edition Copyright © 1992 by Houghton Mifflin Company.

In my country, Canada, we are taught that whole numbers are 0, 1, 2, 3, ... so obviously there are different definitions out there, and hence "dispute".

The numbers you refer to are called integers. Why would we need another official name for the integers? 207.189.230.42 20:09, 23 October 2006 (UTC)

There is indeed disagreement. In my Irish primary school, the whole numbers were given as 0,1,2,3.... My mathematics dictionary (James & James) gives all three definitions, with 0,1,2,3,... as the first.--Malcohol 11:03, 25 October 2006 (UTC)

Should this article just be a redirect?

I've just removed duplicate reference to "nonnegative integer" and disambig template from the article. But what's left is almost nothing! Perhaps it should just be a redirect page. Mitch Ames (talk) 13:02, 25 February 2009 (UTC)

You shouldn't have removed these, because the term apparently is used in all these ways, which is the point of the disambig. I have reverted. --Trovatore (talk) 20:44, 25 February 2009 (UTC)

I added references to the article--in comments--showing the three ways "whole number" has been used by mathematicians. If people believe that references are OK on a disambiguation page, they can be incorporated into the visible text. If not, at least they will be seen by people who go to edit the article, and maybe there will be fewer back-and-forth changes to it.--BrianH123 (talk) 13:29, 19 June 2009 (UTC)

Explanation for the confusion

On the occasion of another edit today that mistakenly removed one of the three meanings, I thought I'd leave here my explanation of where they all come from. This is all conjecture.

Original meaning (presumably)

The straightforward meaning of the term is integer: A (real) number is "whole" if it doesn't involve any fractions, i.e. if it is one of the numbers ..., -2, -1, 0, 1, 2, ...

In schools: Since English has the more popular Latin word integer, the term whole number is redundant if used in this sense. In schools it makes sense to introduce only one word for integers, so whole number is not used in the sense of integer.

In research level mathematics: The literal German translation is ganze Zahl, which is the only German word for integer. This may contribute to the continued use of the word with this meaning in research level mathematics.

Most common meaning

The most common meaning seems to be that of non-negative numbers 0, 1, 2, ... There may be a French connection, since (according to Wikipedia) French uses the following terminology: entier relatif = integer, entier positif = non-negative integer, entier négatif = non-positive integer. With such a terminology it's not entirely clear whether whole / entier is understood to refer to all integers or just non-negative integers.

With the traditional definition of natural numbers as 1, 2, 3, ..., there was no simple term referring to 0, 1, 2, 3, ... So it makes sense to use one of the arguable French meanings of whole number and define them as the non-negative integers.

In schools: It seems that this is the standard definition in many English-speaking schools.

Positive integers

This meaning may be caused by mistranslations from French. The French word positif means non-negative, and plus grand que means greater than or equal. Interpreting positif incorrectly as positive, we get a definition of the whole numbers (entiers positifs, i.e. 0, 1, 2, ...) as 1, 2, 3, ... In connection with the version of the definition of natural numbers that includes 0, this fills an obvious gap in the terminology. This definitions seem to be rare.

Conclusion

One thing that is missing on this disambiguation page is usage advice. People want to find one definition here. If we present three they are unhappy. If we had sources supporting my conjectures, then we could prioritise the definitions and write something like this:

In school mathematics, a whole number is always a nonnegative integer, i.e. one of the numbers 0, 1, 2, ... In other contexts the term may also occur as a synonym for integer. [Footnote: According to a rare third definition, the whole numbers are the positive integers 1, 2, 3, ...]

This could perhaps be added to integer, and the present article be turned into a redirect. Hans Adler 22:41, 20 August 2009 (UTC)

Whole numbers include 0, natural numbers don't

In primary school (United States) I was taught that there was a difference between Whole numbers, natural numbers, and integers. Natural numbers were {1, 2, ...}, whole numbers were {0, 1, 2, ...} and integers were {... -1, 0, 1, ...} - it seems like we should mention this distinction on this page unless it was unique to my education. Scott Ritchie (talk) 23:14, 24 November 2007 (UTC)

I agree. In elementary school I was taught Whole numbers = non negative intergers (0, 1, 2...); Natural numbers = positive intergers (1, 2, 3...). My daughter's text book shows exactly the same thing. Many others have testified the same on this page. Apparently these are the standard definitions taught in the US. Why its not mentioned on this page, I dont know. Surely there must exist a source confirming this. —Preceding unsigned comment added by Racerx11 (talk • contribs) 00:21, 18 August 2010 (UTC)

Oh, lots of sources. The problem is there are also lots of sources that contradict it.

This is the situation: Yes, primary/secondary-level math education in the United States uses the terms as you say, at least in my experience (there could certainly be exceptions somewhere).

Scholarly usage is different. Some mathematicians use the term natural number in a way that excludes zero; others, in a way that includes it. The term whole number is almost never used by mathematicians.

The writers of math texts for K-12 education in the United States seem to have picked one convention and stuck with it, in order to avoid confusing students unnecessarily, but here you see the downside of that choice — they've left their students unprepared to deal with the variety of conventions that occur in the literature.

In an encyclopedia article, it's not appropriate to favor the math-ed convention just to avoid confusion on the part of K-12 students. If anything we should gravitate towards scholarly usage, but as I've mentioned, there is no single convention in that environment either. So the best we can do is explain the situation, which is what this page is for. --Trovatore (talk) 18:50, 18 August 2010 (UTC)

Ok thanks, I understand. I should clarify I meant, "There must be a source confiming this is how US schools define whole number". My point is the situation isn't really explained. Could we put your explaination here as a lead in to the definitions listed in the article? I think it should be noted in the article that one convention is prefered by our education system and how "whole number" is a term rarely used by mathematicians. Its been suggested maybe this should just be a redirect to the natural numbers page, to a short paragragh explaining all this about whole numbers within the natural number article. As it stands now any reader visiting this page is going to be even more confused unless they happen to read the talk page to get the full story.Racerx11 (talk) 02:53, 19 August 2010 (UTC)

I guess that's not an entirely implausible solution. The problem with it is, when an editor links to whole number in some other article, he probably should really link to either natural number or integer instead; it's not likely that what he wants is a discussion of math ed in the United States. Wikipedia is not supposed to be a dictionary and I doubt that a discussion of the locution whole number is really very close to its mission. But I don't feel that strongly about it; a redirect to a section in natural number wouldn't be terrible. --Trovatore (talk) 08:58, 19 August 2010 (UTC)

The term "Whole Number" is a part of math learning.

Student textbooks for at least the last 4 decades in American education have used the term "Whole Number" on average in at least 5 grade levels. Usually from grade 4 through 8. Whereas the term "Natural Number" appears only in 9th and 11th grade materials. It is sad that writers for Wikipedia discredit it, by showing a lack of understanding what is really going on in the classroom.

Jim kelly

www.k-12math.info

I was introduced to the terms "Whole Numbers"(0,1,2..) and "Natural Numbers"(1,2,3...) at the same time, well before the 9th grade. This was about 3 decades ago in a US school.Racerx11 (talk) 00:39, 18 August 2010 (UTC)

I assume it was your teacher who introduced the word "Natural Number", as I have been checking for the presents of 1,000 terms ("Natural Number" being one) in student's K-12th grade textbook series for at least 40 years (one of the functions of k-12math.info). Do you remember the series being used?

Jim Kelly

Could you explain your point please? Perhaps you are trying to push one of the three meanings as the only "correct" one? If so, I have never seen any of the textbooks you are referring to, so I have no idea which of the three meanings you think is the correct one. If I were allowed to dictate the content of this article in order to unify terminology, I would define whole numbers as all integers, because that meaning is etymologically closest to the terms and it's also the correct translation ganze Zahl, the only term for integers in German.

Or perhaps you want the article to say something like the following? "In the US education system, the term whole number always refers to ..." That would be an excellent addition to this page, although (1) we would need a reference for that fact (not just to a textbook or syllabus defining the whole numbers in this way but to someone who says it's like that in the US), and (2) this kind of information is strictly not permitted on a disambiguation page per our formal guidelines. (Not that I would mind it, though.) Hans Adler 11:31, 7 September 2010 (UTC)

PS: Re-reading earlier discussions on this page, it now seems clear that you were referring to the definition of the whole numbers as 0,1,2,... . My comments in the section above this one still apply, especially under the heading "Conclusion". Give me the sources, and I will turn them into an article. But I can't write an article based on other people's personal experiences. In fact, I am not even allowed to do so based on my own. See WP:Verifiability. Hans Adler 11:39, 7 September 2010 (UTC)

Uh yeah not sure what happened. My comment above was directed at the user who initiated this section and that users comment is now gone. So to answer your question, no I dont have a point and therefore can't explain it. I was simply trying to help someone else. Do you know if you can pull up the edit history for talk page in order to retrieve the deleted post I was responding to? Otherwise I honestly can't remember precisely what I was talking about. I think the user was talking about when these concepts were introduced to math students and he seemed to somehow believe it was in the 9th or 10th grade for most students and maybe something about how this has changed over the years. I don't know why his original comment was deleted and the section he created remains.Racerx11 (talk) 16:34, 30 October 2010 (UTC)

I've restored the deleted material. Algebraist 16:46, 30 October 2010 (UTC)

Thank youRacerx11 (talk) 17:16, 30 October 2010 (UTC)

And to Hans Adler it appears that you were also refering to the same deleted material as I. Sorry I got really confused there for a while.Racerx11 (talk) 17:30, 30 October 2010 (UTC)

Usages among mathematicians seem to vary. Among mathematical logicians, the term "natural number" seems to mean "nonnegative integer" (thus including 0), but some others reserve the term for strictly positive integers. I think I've seen "whole number" used to mean "integer", thus including negative integers, but not including non-integers. Michael Hardy (talk) 21:16, 7 May 2011 (UTC)

Reverts

Nobody of you three provided a solid reason for your reverts. Heck, you did not even provide any falsifiable reason why my edits were wrong! How can I argue with a person whose only argument is "I don't think that..." ? My text is based on references to books. Max Longint (talk) 00:22, 7 May 2011 (UTC)

No one is arguing against your content, and therefore the references are irrelevant. This is an organizational question, not a content dispute. The longstanding status, which seems to have reasonably wide acceptance, is that whole number is to be a disambig page, not an article. (Some would even like to make it into a redirect.) Disambig pages are navigational aids, not places to put content, no matter how well-referenced. --Trovatore (talk) 00:26, 7 May 2011 (UTC)

This is crazy logic. What is wikipedia but new content? How references are irrelevant? Since you refuse to dicsuss the content, you are nothing but a bully who has no respect to other contributors. And I no longer want to edit. Max Longint (talk) 00:30, 7 May 2011 (UTC)

No-one is bullying you. It was asked reasonably, given the WP:3RR policy, that you explain your editing, and develop a consensus. Meph^talk 00:37, 7 May 2011 (UTC)

I don't see what to explain. I don't know what is wrong with my text besides an unexplained refusal to accept it. Consensus requires dialog, not stonewalling. Max Longint (talk) 00:53, 7 May 2011 (UTC)

I think I have explained my position clearly, although not on this page. Let me rephrase it carefully here. The term whole number is used in different ways by different people, but in no case does it mean anything interestingly different from concepts treated elsewhere.

Specifically, it can mean positive integer, nonnegative integer, or simply integer. For the first two, we have the natural number article, whereas for the last one, we have integer. Any discussion of whole numbers themselves (as opposed to the phrase "whole number") belongs in those articles. The phrase "whole number" is not interesting enough to have an encyclopedia article about, WP not being a dictionary and all that. --Trovatore (talk) 01:30, 7 May 2011 (UTC)

I support this revision; it makes the point that there are three definitions without belaboring matters which are better treated at the linked articles (integer and so on). See WP:DISAMBIG for the style to follow. As for the references, having them in comments seems like a decent compromise in terms of being able to show to editors why this is a disambig without boring readers with references which are just about terminology. Kingdon (talk) 01:44, 7 May 2011 (UTC)

Wikipedia is an encyclopedia, not a dictionary. We organise our articles primarily by topics, not by terms that refer to them. Terms that can refer to several topics tend to be a problem. I don't have a big problem with Max Longint's changes, but we have a lot of bureaucracy fans who tend to go crazy if something in article space doesn't fall neatly in one of the three categories as (1) a proper article, (2) a disambiguation page, or (3) a redirect. Therefore any hybrid between a proper article and a disambiguation page, as proposed by Max Longint, is automatically unstable. We can't have yet another article on this topic, per WP:CFORK, so it must be a disambiguation page. Hans Adler 08:29, 7 May 2011 (UTC)

I'm by no means a bureaucracy fan, but I do indeed think that no middle ground can be tolerated between an article and a disambig page. They have completely different functions.

In any case I don't think that's the issue here; I think Max was trying to make it an article, not some middle-ground thing. My view is that it doesn't deserve an article. --Trovatore (talk) 11:01, 7 May 2011 (UTC)

Max Longint, I've just looked up my Collins English Dictionary which is usually quite a good guide to British and International English, and it gives the definition 1. an integer. 2. a natural number. I'd agree with most of the contributors on this page that both are wrong - it just shows how variable things are and that yes, maybe we don't want an encyclopedic article about it.

It's a shame that on one of your first edits you've run into both an exceptional article (disambiguation) and some of the more "robust" editors. Better luck on your next effort! Chris55 (talk) 14:36, 7 May 2011 (UTC)

Color me skeptical that Max is a new editor. If he actually is, then I probably should have approached some elements of the discussion differently. --Trovatore (talk) 20:57, 7 May 2011 (UTC)

[revised next morning] At a disambiguation page we should accept listings liberally. It is not the place for argument whether or demonstration that a particular listing is appropriate (although the disambiguation's Talk may be the place for that). So it really isn't the place for References.

There is scope for a disambiguation page to include a preface longer than the current one-liner and to include See also. In a manner of speaking, those features make a very moderate "hybrid" of a disambiguation and an article.

A hybrid page that is closer to a regular article may be useful, and remain valuable for years, but that shouldn't happen where numerous editors are willing and able, as here. Given the editors, something like the following should happen.

At one of the disambiguation target pages, normally one should be able to learn why that page is a target, so the ambiguous term should appear, and explicit discussion of its usage is appropriate. In particular, there should be some discussion at the target page if there is any evident issue whether the ambiguous term (eg, whole number) really is ambiguous in a way that fits the target (eg, integer). (If there is no discussion in the target page, check the target's Talk.) --P64 (talk) 19:32, 8 May 2011 (UTC)

This seems to be a normal case, so the ambiguous use of "whole number" should be covered, and perhaps sourced, in the target pages integer and natural number. —continued—

I was unable to work out what you were saying. The last paragraph was especially cryptic, I was unable to even parse it. Could you use simpler English please. Dmcq (talk) 20:36, 8 May 2011 (UTC)

Thanks. I have revised in a way that changes the order of the paragraphs too.

There is a serious problem here now: no proper target for "non-negative integers" or "positive integers". Both of those listings include piped links to Sign (mathematics) (which explains non-negative and positive without mention of whole numbers). Instead they should not be linked at all. I will rewrite them to make natural number the target for both.

Natural number does cover "whole number" succinctly in the lead paragraph, which does minimally satisfy one normal expectation of anyone who follows those two disambiguation links. (That lead paragraph is unusually redundant. Its revision may be in progress.)

At the moment there is no coverage of "whole number" at integer.

I wonder whether some pages should include a note on terminology as a separate section, perhaps just before See also. --P64 (talk) 15:57, 9 May 2011 (UTC)

I see, this disambiguation page should point to natural number instead of the section within sign. I hadn't noticed it was pointing at sign. That would cover the first two cases and has the exct same problems whole number has with zero. I'll go and change the disambiguation. Dmcq (talk) 16:13, 9 May 2011 (UTC)

Alternative version

[This is my version. I depart after two edit conflicts with Dmcq and suffering exceptionally slow service at this site.--P64 (talk) 16:34, 9 May 2011 (UTC)

Whole number is a term with inconsistent definitions by different authors. All distinguish whole numbers from fractions and numbers with fractional parts.

Whole numbers may refer to:

• natural numbers in sense (1, 2, 3, ...) — the positive integers
• natural numbers in sense (0, 1, 2, 3, ...) — the non-negative integers
• all integers (..., -3, -2, -1, 0, 1, 2, 3, ...)

See History of natural numbers and the status of zero for some more information.

Seems okay to me. Much better than sending them to sign. Dmcq (talk) 17:33, 9 May 2011 (UTC)

Done. This replaces the entire visible content of the page. The long hidden comment remains, documenting all three uses.--P64 (talk) 13:40, 11 May 2011 (UTC)